Particles of uniform size and shape have uses in numerous chemical and mechanical applications, especially when the shape is spherical. For example, toner particles for use in xerographic development systems should, for maximum efficiency, be as near spherical as possible and display a very small size variance pattern. Toner exhibiting such characteristics is also extremely useful in the testing and analysis of xerographic-type sub-systems which act with or upon particulate materials.
Lord Rayleigh first demonstrated that liquid jets exhibits a natural instability and break into segments of random length. He showed further that when a periodic pressure disturbance is coupled to a small liquid jet there occurs, over a certain frequency interval, a growth of the perturbation which ultimately causes the jet to break up into uniform segments. These segments are reshaped by surface tension into uniformly sized spheres. Optimum segment lengths or wavelength (.lambda.) was found to be related to the radius of the jet (a) by .lambda. = 9a. At this wavelength the disturbance has a maximum growth rate. Controlled breakup is possible, in principle, for all wavelengths larger than the circumference of the jets (.lambda. &gt; 2 .pi. a ), but experimentally it has been found that the condition 7a &lt; .lambda. &lt; 36a must be satisfied in order to produce coherent breakup. See, for example, J. M. Schneider, N. R. Lindblad, C. D. Hendricks, Jr., and J. M. Crowley, Journal of Applied Physics, 38, 2599 (1967).
Broadly, the Rayleigh mode droplet formation technique can be seen in FIG. 1. A solution 3, consisting of the material to be sprayed, dissolved in a suitable solvent if necessary and dyed or pigment loaded as desired, is sealed under pressure in vessel 1. An opening in the vessel is covered by an aperture plate 4 which contains an array of holes. Within the enclosure of vessel 1, and at least partially submerged in solution 3, is the radiating face of an ultrasonic transducer 2.
A liquid jet of velocity V.sub.j is formed at each of the apertures by the hydrostatic pressure in the vessel 1. The acoustic signal from the transducer 2 modulates the pressure at the apertures and causes a perturbation in the jet. If the wavelength (.lambda.) of the perturbation is within the limits 7a-36a, the perturbation will grow and cause the jet to break up coherently.
Each volume (.pi. a.sup.2 .lambda.) of the jet is then converted by surface tension into a droplet of volume (4 .pi. R.sup.3 /3), where R is the droplet radius. Since coherent breakup is possible over a wide range of wavelengths, without varying any other parameters the volume of the droplets obtained can be controlled by modifying the frequency f of the acoustic perturbation, since .lambda. = V.sub.j /f.
After the solvent contained in the droplet is removed by evaporation under the appropriate conditions, a virtually perfect solid, spherical particle remains. The size of the sphere thus produced depends not only on the size of the original liquid sphere, but also on the various concentration of the materials in the sprayed liquid.
Final particle size may therefore be controlled by either acoustical drive frequency, jet velocity (vessel pressure), material concentrations and/or aperture size. Of these controlling variables, aperture size by far provides the greatest control range; final particle size will, in general, be on the order of the size of the aperture.
After breakup of the liquid jet, an array of equal sized droplets is formed. When an array of apertures is used, the droplets will vary in size somewhat from jet to jet due to aperture size variation. However, apertures such as those existing in electro-deposited nickel screens have a small size variation (for example, those available from Buckbee-Mears Co., St. Paul, Minn.). Therefore, at the time of droplet formation, the droplet size distribution is quite small.
The regularity of the droplet array is eroded by air drag on the particles; this may result in a collision between two or more particles, which in turn will cause these droplets to coalesce into new droplets with two, three, or more times the volume of the original droplets. The coalesced droplets with their increased size result in a reduction in the overall particle size uniformity.
Stroboscopic light sources and microscopes have been used in the past to observe this breakup; however, when the jet radius becomes very small (on the order of 5.mu.m) these observations become rather difficult. The minimum fluid velocity necessary to form a jet increases as a .sup.-.sup.1/2, and therefore if it is desired to meet the condition .lambda. = 9a, the frequency (f = V.sub.j /.lambda.) increases, not only as a decreases, but also because the minimum workable jet velocity increases. Typically, for a 5.mu.m radius jet working at 10 meters/second, the optimum frequency is 220 KHz. Most conventional stroboscopes have a maximum operating frequency of 2500 Hz, so that it is necessary to synchronize the stroboscope on a large subharmonic of the drive frequency. This limitation and the image smearing caused by the high particle velocity, small particle size, and finite light pulse length can make observations quite difficult and confusing. Recent wide bandwidth electro-optic modulators allow stroboscopic observations at much higher frequencies, but they require more complex equipment. Finally, the required microscopic observations are difficult to make. A 5.mu.m radius jet produces droplets on the order of 9.mu.m in radius; these small particles are hard to observe with telescopic microscopes because of their low magnification. Conventional microscopes with small working distances are ruled out because the spray tends to coat the objective.
An array of uniformly sized, uniformly spaced droplets such as produced by an assembly of parallel jets operating in the Rayleigh mode produces a well-known light diffraction pattern. However, it should be noted that if the frequency of the acoustic disturbance is tuned beyond the region where coherent breakup is possible, the pattern disappears abruptly. The diffraction technique described herein greatly simplifies measurement of all the important particle and jet parameters. It furthermore provides a measure of overall sprayer performance, i.e., particle size uniformity.